Answer to Question #23484 in Abstract Algebra for sanches

Abstract Algebra

Question #23484

Let k ⊆ K and G be as above. Show that a kG-module M is semisimple iff the KG-module MK = M ⊗k K is semisimple.

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Related Questions

1. Let k ⊆ K be two fields and G be a finite group. Show that rad (KG) = (rad kG) ⊗k K.
2. Show that if k0 is any finite field and G is any finite group, then (k0G/rad k0G) ⊗k0 K is semisim
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